Towards Certified Management of Financial Contracts

Abstract

Banks and financial institutions nowadays often use domain-specific
languages (DSLs) for describing complex financial contracts, in
particular, for specifying how asset transfers for a specific contract
depend on underlying observables, such as interest rates, currency
rates, and stock prices.

The seminal work by Peyton-Jones and Eber on financial
contracts shows how an algebraic approach to contract
specification can be used for valuation of contracts (when combined
with a model of the underlying observables) and for managing how
contracts evolve under so-called fixings and
decision-taking, with the contracts eventually evaporating into the
empty contract, for which no party have further obligations. The ideas
have emerged into Eber's company LexiFi, which has become a
leading software provider for a range of financial institutions, with
all contract management operations centralised around a
domain-specific contract language hosted in MLFi, a
derivative of the functional programming language OCaml.

In this paper, we present a small simple contract language, which
rigorously relegates any artefacts of modelling and computation from
its core. The language shares the same vision as the previously
mentioned work with the addition that it (a) allows for specifying
multi-party contracts (such as entire portfolios), (b) has good
algebraic properties, well suited for formal reasoning, and yet (c)
allows for expressing many interesting contracts appearing in
real-world portfolios, such as various variations of so-called barrier
options.

We show that plenty of information can be derived from, and useful
manipulations defined on, just the symbolic contract specification,
independent of any stochastic aspects of the modelled contracts.
Contracts modelled in our language are analysed and transformed for
management according to a precise cash-flow semantics, modelled and
checked using the Coq proof assistant.

Implementations of the contract language in Haskell and Coq are
available online together with
machine-checkable proofs (in Coq) of the key properties of the
contract language.